{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8ae54773-ebff-4822-a57d-6a01d9741809",
   "metadata": {},
   "source": [
    "Chapter 04\n",
    "\n",
    "# 非线性回归\n",
    "Book_7《机器学习》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c2f0ba58-b7f0-45d1-aea7-72b415f40938",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import FunctionTransformer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4d37b43c-35bc-456b-9ba8-e29b0f0fc6c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = plt.rcParams\n",
    "p[\"font.sans-serif\"] = [\"Roboto\"]\n",
    "p[\"font.weight\"] = \"light\"\n",
    "p[\"ytick.minor.visible\"] = True\n",
    "p[\"xtick.minor.visible\"] = True\n",
    "p[\"axes.grid\"] = True\n",
    "p[\"grid.color\"] = \"0.5\"\n",
    "p[\"grid.linewidth\"] = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0d371b19-16ba-48a3-a456-7ededd316e5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "\n",
    "def func_exp(x, a, b, c):\n",
    "    # exponential function\n",
    "    \n",
    "    return a * np.exp(b * x) + c\n",
    "\n",
    "\n",
    "def func_log(x, a, b, c):\n",
    "    # log function\n",
    "    \n",
    "    return a * np.log(b * x) + c\n",
    "\n",
    "\n",
    "def generate_data(func, *args, noise=0):\n",
    "    \n",
    "    # generate data\n",
    "    xs = np.linspace(1, 6, 50)\n",
    "    ys = func(xs, *args)\n",
    "    noise = noise * np.random.normal(size=len(xs)) + noise\n",
    "    xs = xs.reshape(-1, 1) \n",
    "    ys = (ys + noise).reshape(-1, 1)\n",
    "    return xs, ys"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55ffe7cc-b354-4b32-8633-9a6a027d287e",
   "metadata": {},
   "source": [
    "## Fit exponential data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3b35f46d-7284-48aa-9bad-0d4cd4020e0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate data\n",
    "x_samp, y_samp = generate_data(func_exp, 2.5, 1.2, 0.7, noise=10)\n",
    "\n",
    "transformer = FunctionTransformer(np.log, validate=True)\n",
    "\n",
    "y_trans = transformer.fit_transform(y_samp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3afd58f-dc34-40af-9f9b-1ebbe64dbb5b",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b1053e22-9932-491f-9f30-a2e45ab428d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "regressor = LinearRegression()\n",
    "results = regressor.fit(x_samp, y_trans)\n",
    "model = results.predict\n",
    "y_fit = model(x_samp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d9331d33-ca71-4345-80b8-79693ba9f9c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(121)\n",
    "plt.scatter(x_samp, y_samp)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.scatter(x_samp, y_samp)\n",
    "plt.yscale('log')\n",
    "plt.ylabel('ln(y)')\n",
    "plt.xlabel('x')\n",
    "plt.grid(True)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1242885-cba3-4ca9-997e-d717244a7238",
   "metadata": {},
   "source": [
    "## fitted data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cf418424-11ba-4bb7-9ae4-f604f033acdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(121)\n",
    "plt.scatter(x_samp, y_samp, label = 'Data')\n",
    "plt.plot(x_samp, np.exp(y_fit), \"r\", label=\"Fitted\")\n",
    "plt.legend()\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.scatter(x_samp, y_samp, label = 'Data')\n",
    "plt.plot(x_samp, np.exp(y_fit), \"r\", label=\"Fitted\")\n",
    "plt.yscale('log')\n",
    "plt.ylabel('ln(y)')\n",
    "plt.xlabel('x')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2ee19500-8a40-4296-8850-109df045500b",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Fit log data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b3808ea-1df7-4534-aa2c-9947f134e96f",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "38318a7e-188d-4313-8bf3-d602d796e207",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_samp, y_samp = generate_data(func_log, 2.5, 1.2, 0.7, noise=0.3)\n",
    "x_trans = transformer.fit_transform(x_samp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f0002fc-0de2-4342-a588-ef66ee424863",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "85632713-52a0-46f6-afc6-8398fe9ed2d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "regressor = LinearRegression()\n",
    "results = regressor.fit(x_trans, y_samp)\n",
    "model = results.predict\n",
    "y_fit = model(x_trans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "edd46752-6ad0-4603-9f6b-b7deecb829e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(121)\n",
    "plt.scatter(x_samp, y_samp)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.scatter(x_samp, y_samp)\n",
    "plt.xscale('log')\n",
    "plt.xlabel('ln(x)')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcf9380e-9ff8-45f1-a15a-096e5b63990a",
   "metadata": {},
   "source": [
    "## fitted data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0ab22af2-0356-4d5b-aa11-c3e95061a702",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAxYAAAGGCAYAAADmRxfNAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAA9hAAAPYQGoP6dpAAByvklEQVR4nO3deVxU9f7H8dcAAoKCK6FmapYW2WZpWlZaWpapLVq5lFaaKe11W2+p9Wu1unaTbLGbFTdLW9Vutuoty4VSS8OuZqaGGIYKyM7M/P44gSIMzH7OzLyfj8d9XGY4M/M9o523n/PdbE6n04mIiIiIiIgPosxugIiIiIiIhD4VFiIiIiIi4jMVFiIiIiIi4jMVFiIiIiIi4jMVFiIiIiIi4jMVFiIiIiIi4jMVFiIiIiIi4jMVFiIiIiIi4rMYsxvgLYfDwc6dO2nevDk2m83s5oiIhByn00lRURHt27cnKir07zMpF0REfONrLoRsYbFz5046duxodjNERELejh07OPzww81uhs+UCyIi/uFtLoRsYdG8eXPAOPGkpCSPX79gwQJGjhzp72ZZXiSedySeM0TmeUfiOYP3511YWEjHjh1rrqehTrkgIuIbX3MhZAuL6m7upKQkrwIkISHBq9eFukg870g8Z4jM847Ecwbfzztchg0pF0RE/MPbXAj9QbUiIiIiImI6FRYiIiIiIuIzFRYiIiIiIuKzkJ1j4S673U5lZWWd55s0aUJZWZkJLTKXp+fdpEkToqOjA9giEZHgUi74LjY2NiyWKBYR/wq5wiIjI4OMjAzsdnuDxzmdTnbt2sW+ffvq/X3nzp3ZunVrAFpobd6cd4sWLUhNTQ2bCZ4iEl6UC8EXFRVFly5diI2NNbspImIhIVdYpKenk56eTmFhIcnJyS6Pqw6PlJQUEhIS6vyjeO/evbRs2TLQzbUcT87b6XRSUlJCXl4eAO3atQtk00REvKJcCK7qjQhzc3M54ogjdNNJRGqEXGHhDrvdXhMerVu3rveY2NhY4uPjg9wy83l63k2bNgUgLy+PlJQUDYsSkZCkXPCvtm3bsnPnTqqqqmjSpInZzRERiwjLwqJ67GxCQoLJLQkP1d9jZWWlCgsRN9kdTlZv3UNeURkpzePp3aUV0VG6s2sW5YJ/VQ+BstvtKixEAijUsiQsC4tq6p71D32PYgWhdHFdsiGX6YuyyS04MBG4XXI8U4emMbiHhhSaSdcz/9D3KGIIZDaFYpaEdWEhIuEhlC6uSzbkMjlzDc5Dnt9VUMbkzDXMHtvTcm0WERHPBTKbQjVLTC8sSkpKeP3117HZbHTt2pWBAwea3SRTPfnkk7Rq1arO86eeeirLly/nxhtvDMjnLl++nMMPP5zOnTsH5P1FvGWFi6u7d6TsDifTF2XXaSuAE7AB0xdlMygt1aM7WqHUW+MvyoYDlAsi1uPvbDr4Ot8mMY5pC93PEitlhKmFRVVVFTNmzOCOO+6gWbNmZjbFMtq3b8/YsWPr/d1JJ51U83NmZmat43777Td+//13+vXrF+gmigRNoP6h7glP7kit3rqn1nH1tTm3oIzVW/fQt2v9E4h9+fxwoWyoTbkgYi3+zqb6rvMNOThLCkorLJURpu5u8+abbzJlyhQFh4jUy5N/qAdC9R2pQ9tQfUdqyYbcWs/nFbkXCu4e5+nnhwtlg4hYmT+zydV13h2fZe+yXEaY2mNRUlJC27ZtzWxCSKm+G7VgwQKWLVtGWVkZJ554Ik2aNOGTTz5h7969bN++ndGjRwPw3//+lw0bNpCQkEBRUVGtO1lLly5l7dq1NGvWjKqqKtq1a8fhhx9u1qmJ1Mvf/1D3hDd3pFKau7dUqTvHefL54UbZ4D5/5EL1MCvlgoh7/JVNDV3n3fHBup2m9ujXx7TCoqKigoSEBJYtW8a2bduw2+2kpaXRp08f/3+Y0wklJbWfKy6GYKxXnpAAfl49Y+TIkZSXl9cqFFq0aFGry3vLli0UFhaSnp4OGEsCvvzyy4wcOZKSkhK2bdvG7bffXvP6W265hZNPPtmv7RTxlT//oe4pb4Y19e7SinbJ8ewqKKv3Ym8DUpON8a/+/PxwYmo2RGgu3HDDDcoFEQ/4K5sau867YgNaJjZhT3GFy2O8GXrrD6YVFvn5+axatYozzzyT/v37A8bdkm+++YYzzjijzvHl5eWUl5fXPC4sLHT/w0pK4JAu9aB9xfv3Q2Ki24fn5OTwwgsv1HouJSWFSy+91KOP/eabb7j66qtrHkdHR9OmTRvsdjtLliyp837Dhw/36P1FgsGf/1D3lDd3pKKjbEwdmsbkzDXYoFabq/8ZOXVomlt3j8zsrTGTJ9ngUy5AnWxQLigXRNzhr2zy5vpdnR6XnNSBV775rdHjg50RphUW5eXlDBw4kC5dutQ8N2DAAObOnVtvYfHYY48xffr0Os8vWLCgzoZHTZo0oXPnzuzdu9fYxKe4OHiBcYj8/Hwoc/8PNSkpiZEjR9b7PkVFRcb7Qa2fAfbu3UtBQUHNcz///DOzZs2q8x49evTgjz/+oLKystbrS0tL2bt3L82bN6/z2RUVFRQXF7N48eKaTaZCSU5ODvPmzTO7GUEXLud9ZesyfiwtcPn7E1onM//ttwD/nvPe4grOjd3b6HE53/3JvI2xtZ679cgyNu3aT1mVvea5+JhouqU2Y+/6Zcxb79/PL9m326vzLjm0J9cCPMkGn3IBTMsGq+XCySefHHG5IOIrT7LJFXev8werzpImf/zpdUY1xNdcMK2wiI2NpUWLFnWed7Wz87333luri7awsJCOHTsycuRIkpKSah1bVlbG1q1badmyJfHx8dCqlXGH6CD5+fm0bh34SGntYZd38+bNXbbr4N8delxRURHFxcU1zx177LFcddVVdd4jPz+f5OTkOp+RnJxMy5Yt6/3ssrIy9u3bx0UXXWR8nyFm3rx5jBo1yuxmBF04nbe7KyP585ztDif9nviy0TtSL117jsulZ31Z/s+Tz5//9ltenXdhYSETJkzw+HWB5Ek2+JQLUCcbIjUXgIjLBRF/8HXVPneu84clxfH05Sfx5/7yWlnia0a54msumFZYHHbYYXz11Vd1nnd15yMuLo64uDjvPsxmq9vtXFbmUVd0qDl4eMChEhMTKSoqqvculIgVDe7RjkFpqUFdp9vXYU3RUTafxrX6c1hVKPEkG3zKBaibDcoF5YKIB3zNJneu89OGHccZR7Xx6rVmZIRpy81GR0dTWlpaq8tl27ZtWl7QTQ6Ho9bjZs2a1RpfPHDgQN58881ax2zatAmA8847j3fffbfW7z7++OMAtVTEP6r/oT78pA707dq60Yul3eFkxZZ8PlyXw4ot+dgdnq+7MbhHO2aP7Ulqcu07sqnJ8UHZmM/szzeDssF7ygWR4GssmxrLIl+u8w2+dszJpmSEqcvNjh07ltdffx273Y7T6SQqKspy3fJW1adPH5555hnS0tIYPHgwbdq0YePGjeTk5DB27Fg6d+7Mrl27mD17NgkJCVRWVnLSSSfRunVrmjZtSufOnfnHP/5BYmIidrud4447zuxTEvEbf24qZ0Zvidufv349vPIKJ/z2G4TJsDdQNnjL21wAlAsiAeBuFvmSM3Ve2yyO095+kaiZb8KcOX5fga4xNqfT6e3yuaYqLCwkOTmZgoICl2Npu3Tp4nLsZ7DG0lqNN+ftzvdpZeE018ATkXje8+bNo+Xx/ZmcuabOmNPqS2vI3+kvLIS33zYCY/VqAMqaNuWH1f/j1LTDPR5L6+o6GoqUC8ET6rkgEmjVG98FNYtKS3Fcex1RbxmLefz0xnscM/rioOaCqTtvi4j4k9NJg5vKgfF7b4ZFmcrphG+/hWuvhXbt4PrrYfVqqqKiWdKtLy8MH8uo19fS74kvw3Y3bhGRUNHYBqcQgCzauZN9vU8n6q15VEZFc9/56QzZEBv0XFBhISJhY19JRXhtKpefD//4Bxx3HJxxBrz6KpSUsL9zVx7tfy19pszlhkvuZ/3RaTiiotlVUMbkzDUqLkRETBT0DU6/+46yk0+hxYZ17I1vzlVXPMybJ10AEPRcMHWOhYiIP5XbHY0fhMU3lXM4YNkyePlleO89qPhrZ9WEBLjiCuzXXMugr8vILay7wo8To5t9+qJsBqWlht2KUSIioSCoG5y+/TbO8eOJLytjU+sjuG7Eg+xokVrz62DngnosRCRsxEW7d0lLaW7BMeF5efDEE9CtG5x7Lrz1llFU9OwJs2dDbi7861+sbn9svUVFtZDrlRERCTPuZoxPWeRwwIMPwpVXYisr44uuvbj0qqdqFRXVgpkL6rEQkbDRIiGWdsnxjW4Y1LtLq2A3rX5Op9E78cIL8P77UL1XQ/PmMHo0TJwIp5xS6yVBvRMmIiIe692lVWCzqLgYrr7a6NUGNo+7gYkpF+CIqn+T6WrByIWQ67HIyMggLS2NXr16md0UEbEYm83YEAgOrLxR87u//t8Sm8rl58PTT8Mxx8A558D8+UZR0auXsdrTzp1GsXFIUQFBuhMWYpQLImIl1ZvXQQCyaMcO6NfPKCpiY2HuXP584P8aLSogOLkQcoVFeno62dnZZGVlmd0UEbEgy24qV72y01VXQYcOcOedsGkTNGsGN9wAa9YYy8ded53xnAvVd8JcxZENY510y/TKBIFyQUSsJiBZ9O23cOqpsG4dpKTA0qUwbpylckFDoUQk7Ji9qV0tRUWQmWn0QPz444Hne/Y0CopRoxosJA5VfSdscuYabFCrm91SvTIiIhHOr1n02mvGUuMVFXDiibBwIRxxBGCtXFBhYTFPPPEEycnJANhsNkpLS7ngggvo3r27yS0TCS3RUTb6dvVsszO7w+m/YmT9enj+eaOo2L/feK5pU7jySpg82Rj25KXqO2GH7uia6uXu4mJtygWR0OUqi9zOG7sd7r0XZswwHl9yCbzxBiQm1jrMKrmgwsJiOnTowNixY2s99+KLLxIXF0fnzp0bfX1mZmad14tI45ZsyK1zQW7n6QW5osKYhJ2RAV9/feD57t2NYuLqq6FlS7+09+A7YSs/z2PCwD7m9cpIQCkXRMKL23lTWGgs5PHRR8bjBx6AadMgqv6ZDFborQ+5ORaRaNKkSfznP/8xuxkiYWvJhlwmZ66ps6GR2xsL5eQYy/516mT0SHz9NURHw4gR8OWXsHEj3HKL34qKatV3wlKT4unbtbWKigiiXBAJTW7nza+/Qt++RlERHw9vvgkPPeSyqKhWnQvDT+pgSi6ox6IBfh0W4aNmzZrhcDj47rvvWLduHdHR0TgcDnr06EHfvn3ZsmULS5cuZeXKlZSVlXHNNdcQHR3NBx98wO7du4mOjqayspLTTjuN1q09Gx4iEs7sDifTF2XXuyRggxsLOZ3Y//sV+554hpaffUSU3W48n5pqjIO9/npjkraElXDMhcGDB9OpUydTzkEkkribN+f+sRFGjqTJ3j1UpBxG9MKFRJ/WO8it9Y4KCxf8MizCj9q3b09OTg7Z2dlcf/31Nc+/8cYbnHbaaXTt2pWuXbsSHx9f0+WdlZVFp06duPjii2uOz8jI4KSTTgpy60Wsa/XWPXXuHB3s4I2F+nZtDSUl8OabFM74B0mbsqku01d17MGiM4Zz5l0TOf9k/SMtHIVrLrz22muMGzcu2M0XiTju5E3//34Af59NE4edH1KP5vpL7yfqyyKmJuaGxPw5FRb1qO6mOrSirO6mMmPJyvj4eCoqKhg9enSt5zt37szOnTs5/PDD67zmuOOOIyEhodZzMTH6I5eGWemObDC4u2FQ0f82w4tPGPtM7N1LElAaE8f7x/Xn9Z4X8XNKF2zAv9/ewOwmsSERAOK+cM6FJk2aBLSdImazSq41lDfRDjt//3IO13y/CICFx57F3y64hfImcdhMvM54Sv/KPITXwyICrKysjGbNmlFaWsqbb75JVVUVMTExbN68mYkTJ9b7moSEBLZu3cpnn31GdHQ00dHR/PDDD0Frs4Qeq92RDYYGNwxyOjltxwau+X4hg2asAocDgJyWqbx60oUsOH4QBU2bHzgc864REjjhngvr16+vU5yIhAsr5ZqrvEkq28+sD5/grN/WAjDjzKvI6Hu5sesroZUtKiwO4fGwiCDJzc2lV69evPzyy0yePJnEv5YZW758ucvX/PDDD6xfv56JEydi++svZ2lpaVDaK6HHindkg6F6Y6FdBWU15x5XVcGw7GVc8/0i0vK2Hjh44EB+HjmeC39p7nKXU7OuERI44Z4LmZmZQWmvSLBZLdfqy5sue3KY8+5DdN2TQ0mTOG676A4+6XZ6ndeGSrZoVahDuDsswt3j/KW4uJivv/6a66+/viY8wLhj5cqGDRsYO3ZsTXgAlJeXB7SdEpoauyMLxp0Su6O+I0Jb9cZCACn793D7V2/w7fPjmfHxP0nL20ppTBzbR14FP/0En33G/3r3d1lUHCzY1wgJnHDPhYaOFwlVVsy1g/PGBvTbupYPXr+drnty+D2pLSPGzKi3qDiY1bMl5AqLjIwM0tLS6OXD5lINaXBYhBfH+cOrr77KBRdcQMuWLdm+fXvN8+Xl5bz77rtUVlbWPOf4a6gGQGVlZa1CYvv27Q3eyZLI5ckdWauxO5ys2JLPh+ty2Ftc4VVIDK7cxfLsuXzzwrXcvOJtWpcW8ntSW2YNnsi3y9ZwxPzXIe2v4sOC14hIp1zwLReWLl0anEaLBJFZuXZwJq3Ykl8nkwb3aMfsMSdz008fM3fBVJLLi8nqkMa4G2aRfdiRjb6/1bMl5IZCpaenk56eTmFhYc1OpP5UXzfVwWwYuxj27tLK758NsHPnTubMmVPzuLS0lPPPP59OnTrRqVMnXnjhBVavXg1AVVUVU6ZMYd++fbWOf/nll7n44ou59NJLee6552jTpg12u51mzZpx4YUX1ozDFalm1TuyjTl07Oy5sXvp98SX7o2dtdth8WL4xz/gv/+lemHYwlNO4+crr8U+dDiTj06pM5bV7GuE1KVc8C0XLr74YuWChB0zcs2t+RwVFQx+bhqDF78MwPahI7E/PpOPu6Vy9oylIZ8tuoocorqbanLmGmxQ6w+3+p8XU4emBWzizF133dXg72+44YYGfz9p0qRaj++8885aj/Pz8xUeUocV78g2xuuxs8XFMHcuzJwJv/xiPBcTAyNHwm23kdSrFw2tFu7rNcIqq5OI+8I9F0TCUbBzza1MSm0Cl10GX31lTMyeMYMjbr+dI/4amtjYdeaBIcdaPj/0L8x6DO7Rjtlje9apOlPDfHUciVxm35H1lFer9OTmwqxZ8MILsOevru+WLY2N7G68EepZmtMVb68RVlqdRDyjXBAJLcHMNXcy6Y2XP+L8RY9i27oVmjeHt96CCy+sdWxD15lhJ7bj4Y82Wj4/VFi4MLhHOwalpVq+MhTxB7PvyHrKo1V6SnPhmWfg3/+GigrjgCOPhNtvh/Hj4aBJr57w9BrR2N2sjNEn0zIxTtcbC1MuiISOYOZaY5k04JfV/HPRDGwVpUb+LFwIxx1X77H1XWf2FleQ/mbd/MgtKOOGzDXcNvBobjznaEtci1RYNCA6ymbpJb1E/CmU7sg2OibW6aTv9vUcefVT8O2yA8+ffjrccQcMHw7Rja/s1Bh3rxHurE5y47y1HDzHz4p3okS5IBJKgpVrLjPJ6eT61e9xz7K5ROFk96l9abtkEbRu+Bpy8HXG7nDS74kv682Pav/4fDPzVu9g2jDzM0OFhYjUCJU7sq7GxEY57AzZ+DWTVr/LCbv+mj8RFQWXXGIUFH37BrGVBzR2Nwvg0MWswn3/EBGRYAhGrtWXSXFVFTz6ySwu2/AlAP8+aTBd33iVto0UFYdyJz8AdhVaIzNUWIhILaFwR/bQsbPxlWWMXP85N323gJS9+QCUx8TSZOJ1RN1xB3Ttamp7vVl1JJR2WhURsbJA59qhmdSmeC8vvvcIp+z8mSpbFA+fO5FPB4xgebfDPH5vT/PD7MwI68LC6Qy/zbzMoO9RwFqrGVWPnb17zleM+34R475fROvSQgD2NE3i9Z5DOP7R+zj3rB6mtO9Q3q46Eio7rYYSXc/8Q9+jhDp/ZtrB8zmO+2MLL737f3Qo2k1BXCLpF9/LN51PYvaw47x6f0/ywwqZEZaFRZMmTQAoKSmhadOmJrcm9JWUlAAHvleJPJZbzSgnh8Fz/8HAl18gpqQYgO3Jh/FV337M6XMN91zWk3MtNHyosdVJGmO1/UNCkXLBvyr+Wggh2g9zlUSCLRCZNrhHO947LJdjnrmbppVlbGl1OBMue4CyLl2Z7cP7epMfZmZGWBYW0dHRtGjRgry8PAASEhKw2WpXiRUVFZSVRV5Ye3LeTqeTkpIS8vLyaNGihQIkQnm9X0QgbNoETz4Jr78OlZXEAM4TTmDzNen83O98Ctct44trL7TcsKGGVidxh5X2DwlVygX/cTgc7N69m4SEBO2LJCEnIJnmdMLDD3Py1KkA7Os3gJ8fncWj7Q/zuXf/4Pxwl5mZEbZXhNTUVICaEDlUcXFxrZ1JI4U3592iRYua71NCjy/dvV7tFxEI69bBo4/CO+8YF3CAs86Ce+7BNngw3Ww2ugHzNsdarqio5mp1kihb3Ynb1ay2f0ioUy74T1RUFEcccUSd4kzEDO7mXEAyraQErrkG5s83Ht9yCy2eeoohfiy6q/Nj2sKf2FVY7vI4K2RGyBUWGRkZZGRkYLfbGzzOZrPRrl07UlJSqKysrPP7xYsXc9FFFwWqmZbl6Xk3adJEPRUhzNfuXo/2iwjEeM5vv4VHHoH//OfAc0OHwj33GEvHhpiG1icH6+8fYlXKheCLjY0lKirK7GaIeJRzfs+0nBxj+fLvv4eYGHj+eZg40dtTaVB1fsz68hf+8fmmOr+3SmaEXGGRnp5Oeno6hYWFJCcnN3p8dHR0vf8wrqysJD4+8oYXROp5R6K8ojLu87G7191xmn4dz+l0wuefGwXFf/9rPBcVBVdcAffeC8cf77/PMkF9q5PMjgqN/UOsSrkgEpk8Hdbk10zLyjKKitxcY1+Kd9+Fs8/2oPWei46yccvAo+me2syymRFyhYWINM7ucLJp136cpNT5nSfdve6O0/TLeE6nEz76CB5+GFavNp5r0gTGjYO774ajjvL9MywqVPYPERGxCm+GNfkt0+bNg2uvhbIy6NHD2Em7SxeP2u8LK2eGCguRMLR66x7KqlwPC3G3u7ex1Sj8Mp7T4YAPPzQKirVrjeeaNoXrr4c774TDD/f+vUNIKOwfIiJiFd4Ma/I50xwOePBBo0cdjKG5//43NG/u07l4w6qZoQGSImHIX9291atRwIHxm9V8Hs9ptxuT3U48ES691CgqEhPhrrtg61aYOTNiigoREfGMNznnU6bt3w8jRhwoKu6+G95/35SiwspUWIiEIX8OYapejSI1ufaxqcnx3i3LZ7fDW28ZcyWuuAI2bICkJLj/fvjtN3jiCTjM891JRUQkcnibc15l2rZtcMYZRiERG2ssef7446DFberQUCiRMNS7SysyY6KxVdS/Z4KnQ5j8Mp7TbocFC+Chh2DjRuO5Fi3g1lvh5puhZUv330tERCKaL8OaPMq05cuNXvXdu42bXh98AH36+Pt0woYKC5EwFB1lo1tqM/7zK3U2ZPN2CJPX4zldFRS3324UFG6s4uNvvuztISIi5mto41F3cs6tTHv1VZg0CSor4eSTjfmAHTt63eZIyB4VFiJhKqV5fL0bsgVtSTqHw9jQbto0yxQU4PveHiIiYg2uNh71OefsdmO+3zPPGI8vuwxee82YB+ilSMkeFRYiYcyUJemcTuOuztSp8OOPxnMWKCjA8zXPRUTE2vyecwUFcOWVsGSJ8XjqVGMlKB82hIyk7FFhIRLmgrYkndMJH39sXIC//954LinJKChuvdXUggK8W/NcRESsz28598svMGyY0cvetCnMnQuXX+7TW0Za9oTcqlAZGRmkpaXRq1cvs5siItWWLjVWzBgyxCgqEhPhvvuMZWOnTjW9qADP1jyX0KJcEBGfLV0Kp51mFBUdOsDXX/tcVEDkZU/IFRbp6elkZ2eTlZVldlNEZNUqGDgQzjkHVqygKj6enIk3Yt/yq7HWdysfNs7zM3/t7SHWo1wQEV84np+N47zzYM8eik7siX3VajjlFL+8d6RlT8gVFiJiAevXw8UXG0vuffEFldExvHrKUPpe9zJntBpMv3+tZ8mGXJcvtzucrNiSz4frclixJR+7o75OYv/y594eIiISBior2XbleKLSpxBVVcX7af05deDf6ff6xloZ5ktmRVr2aI6FiLjv11+NORRvvglOJ86oKBYcdw7PnjGanOSUmsMampBm1soYvqx5LiIiYWbPHv68cDidVi3HgY0ZZ1/N7NNGgM1WK8MAnzIr0rJHPRYi0rg//oAbb4Tu3eHf/wanE8eIkYy6eQ53XXhrraICDqwnPn1Rdq07O9UrYxw63rT6It5QL4evqtc8hwNrnFfzdm8PEREJQRs34jztNNqsWk5xk3gmXXo/s/uMBJtx/a9OrXveW+9zZkVa9qiwEBHXCguNHoquXSEjA6qq4Pzz4fvvWfX4bFbGpbh86aET0hpbGQPqFiL+Vr3meWpy7S7n1OT4sFruT0REXFiyBPr0wfbLL/yelMJlY2fw2dF1d9J2AvtKKv2SWZGUPRoKJSJ1lZfD7NnGBOw//zSe690bHn8cBgwAIG9djltvVT0hzZOVMQK5PK4pe3uIiIi5nE549lm44w5wOMg/uTfDz7iZ/MQW3r0dnmVWpGSP6YXFlClT6NmzZ83jxMRERo0aZWKLRCKYwwFvvQX33w+//WY81727UWBcemlNNzF4PiHN3RUvdhWUsmJLfkAvvEHb20O8olwQEb+qqIApU+CVV4zH117L5jseJv/1tT6/9Te/7HY7pyIhe0wtLPbv38/555/P8OHDzWyGiICxhvff/nZgc7v27WHaNLjmGoipe6nwdEKau4XIwx9tZE9xRc3jYEzsFutQLoiIX+3eDZddZuxLERUFTz0Ft95KLye0S97oMsPcNWvpFt5dk6Oc+oupcyzy8vJo27atmU0QkZ9+gosuMvai+P57aN7c6KHYvBkmTqy3qADPJ6RVFyKN3dM5uKiA4EzsFutQLoiI36xfD716GUVFUhJ89BHcdhvYbG5lWIuEJo1mFiinDmZqYbF7925SUlxP/hSRAMrNNQqHE04wLrYxMcbKT7/8YuyanZDQ6Ft4MiGtoYt4Q4I1sVusQbkgIn6xaBGcfjps2wZHHQUrV8LgwbUOaSjDXhjbk8cvPR5oPLOUUweYOhRq9+7d5Ofns3z5cmw2G506daJ///71HlteXk55eXnN48LCwiC1UsQ3dofTWpO1SkrgmWeMidjFxcZzl10Gjz4K3bp5/HYNTUg79NwHpaUye2zPOmuCt0pswp7iSpefEayJ3WI+5YJIeApaFjqd8MQTxg0yp9PojV+wAFrVv09EfRl2SqeWfL9tL3lFZdw6sBvzVm9nV2HD8wSVUwab0+k0rbTasGEDMTExHHPMMQD8+OOPbN++nYsuuqjOsdOmTWP69Ol1np8zZw4JbtxZPVROTg4dOnTwvNEhLhLP28xzzisqY9Ou/ZRV2Wuei4+Jpltqs4DvslnnvB0OOn/zDSe8/TaJe4wlYP886ijWjh3Ln14UFI1p6NzbNotnX0kF5XYHcdFRlFU5+GlnQaPv2aNDMqlJrr+3SPz7Dd6fd0lJCRMmTKCgoICkpKQAtMxzygWR8BOsLIyqqOC0l1+m8zffALB54EC+v/pqnC6G9Lrb1riYKJKbxrq1CEljOWV1vuaCqYVFfV577TXGjRtX5/n67kx17NjR6xOfN29eRK4yEonnbdY5V28Gd+h/YNX3ZwK9dnWt8/7qK7j99gMTszt1Mnosrrii1kpP/uLpua/Yks+ol1c2+r7zJvZp8E5QJP79Bu/Pu7CwkOTkZEsVFvVRLoiErqBlYW4uXHIJrFoF0dHwz38aK0H5qa3u/mO5sZyyOl9zwXIb5MW4qCrj4uJISkqq9T8Rq7LCZnCAsWTsyJFw9tkHJmY//jj8/DNceWVAigpvzr2xid02jNWhqleYksiiXBAJTUHLwjVrjL2WVq2Cli3h0089LircaWuUzfV8C+WUwdTC4p133qnzXFSU5WodEY95shlcQOzfz/Hz58Mxx8A77xhL7E2aZEzMvvtuiA9cN6035+7pClMSvpQLIuEjKFm4YAH06we//25k3urVxrwKP7cVwOE02qyccs3Uq3VSUhK//PJLzWOHw0FpaamJLRLxD3c3g3P3OLc5HPDGG9C9Oz0++MDYQXvAAFi3Dl54AYKw2o635+7JClMSvpQLIuEjoFnocBh7LV1+OZSWGis+rVxprADlBXfbcO0ZnZVTDTB1VajzzjuPefPmsWzZMmw2G2VlZYwZM8bMJon4hae7UvvF6tVw881GVzCwv21bmr34Ilx8cUCGPLniy7k3tMKURAblgkj4CFgWFhfD+PFGjzwYcwiffNKYW+Eld9swKC2V+4ekKadcMLWwADRRTsKSp7tS+yQvD+69F/71L+NxYiL8/e981K4dV1xyicuXBWrpP1/PPTrKFtIT38R3ygWR8BCQLNyxA4YPh7VroUkTozf+2mtrHeJNvnnSVuWUa6YXFiLhqHrOwOTMNXVWk/DbWMyqKnj+eXjwQSj4a6nWq6+Gxx6D9u1xzJvn8qVLNuTW2UuiXXI8U4em+dyVG5RzFxERy/N7HqxcafTC//EHtG0L774LZ55Z6xBv803Z5R+aEScSIAGdM7BsGZx8Mtxyi1FU9OwJ33wDr70G7ds3+NLq5fQOnaS2q6CMyZlrWLIh1/t2/UXzJUREBPyYB2+8Af37G0XF8ccbw3/rKSp8yTdll+/UYyESQH6fM7BzJ9xxB7z1lvG4VStjx+wJE9waW9rYcno2jKX/BqWl+nxXRvMlREQEfMwDh8PYRfuJJ4zHw4dDZiY0a1brMH/lm7LLNyosROrhz/kHfhmLWVUFzz0HU6dCUZGxfOwNN8DDDxvFhZs8WfrPH+NHNQ5VRCR8+JKNXuVBURGMGQOLFhmP77vPyL16lqD2Z74pu7ynwkLkEIGcf+Cugy/eXf+3juMeuRfb+vXGL/v0MeZWnHyyx+9r2jK4IiIS0oKVjdX5t//nTZxx+3UkbNoIcXHwyitGkeGC8s0aQm6ORUZGBmlpafTq1cvspkgYCsb8A3fa0O+JL7lx5hIqrhpPjysvwrZ+PRXJLeHll425FF4UFWDSMrgiAaZcEAmsYGVjdf7948E59Bw5mIRNG/mzeStWvPpeg0UFKN+sIuQKi/T0dLKzs8nKyjK7KRJmGhufCcb4TLujviP8Y8mGXKa88R1n//cDvphzAyM3fA7AWyecR5+rZ7Gkz5B6u4DdVb2cnquOaxvGHSi/LIMrEiTKBZHACVY2VhcvZ361kMy3/k7r0kJ+TD2KoWOfYfQPzkaLF+WbNYRcYSESKJ6MzwwEu8PJ63P+w9v/vofHP5lFi7L9ZKd04dKxM7jngpvZm5Ds88W7ejk9oM7FV8vpiYjIoYKRjXaHk//7YD1//+JlnlzyT2IdVSw+5kwuH/04uUltgMaLF+WbNaiwEPmLqeMzS0vJTb+d156bRK+cbIqbxPPwORMYOm4mazocC/ivsNFyeiIi4q5gZOP3P2zlkX/dy3XffQjA0/3GcOOwuyhrYuSUu/mnfDOfJm+L/MW08ZmffgqTJ3P4r78C8NlRpzF10CR2JqXUe7g/ChstpyciIu4IeDZu3syxl15A89+2UBoTx+1DbuPjY/rVe6g7+ad8M5cKC5G/VI/P3FVQVu9YUhvGXQ+/jc/cvRtuuw3+/W8Ayg9rx02nX8un3fo2+DJ/FTZaTk9ERBoT0Gz8/HMYOZLm+/axs3kbJl72AD8d1tXl4e7mn/LNPBoKJfKXoI3PdDqNzX2OPdYoKqKi4Oabifnfz6zvNUATz0RExDICko1OJ2RkwODBsG8fzj59mHjj82S7KCqUf6FDhYXIQQI+PnPbNrjwQrjqKsjPh+OPhxUr4NlniU5O0sQzERGxHL9mY2UlTJkCN94IdjuMHYtt6VJuGm0Mf1L+hTYNhRI5REDGZ9rtMGsW3H8/FBdDXByOBx5g9WXX8UeZnZQt+fTu0qrm4n3oJkSpf21CNCgtlRVb8jVuVEREgsov2ZifDyNGwLJlYLPheOwxVl12HXk/55PSPJ6M0T15+KPa+XdYUhyjeh9BeZWDFX9lpXLPulRYiNTDr+MzN26Ea6+FlSuNx2eeydd/e4S7NlSQO/f7msMO3sG0vov3Z9m76PfEl6buCC4iIpHLp2zMzoahQ+HXX6FZM75/bBY3Fh1O7pxVNYe0S47ngSHH0jIxjryiMn77s4R5q7fzj8831zpGuWddGgolEihVVfD448Yu2StXQvPm8MILLJk1j6u/KWxwB9Pqi/fwkzrQt2trPsveZfqO4CIiIl75z3+gTx+jqOjSheWvL2TE723qzbT0N9dSUFpBXEwUMz/fxK5C5V4oUWEhEggbNkDfvnDvvVBeDhdcAD/9hH3i9Uz/6GePdjC1wo7gIiIiHnM64emn4aKLoKgIzjoL+8pV/O1nR4OZNm3hT0xbqNwLRSFXWGRkZJCWlkavXr3MbopIXZWV8PDD0LMnfPcdtGgBc+fCRx9Bx45e7WBq9o7gIlanXBCxoPJyYxjwnXcaBcaECfDZZ6wuimo003YVltfpqTj0GOWeNYVcYZGenk52djZZWVlmN0WktvXroXdvePBBo8AYNgx++gnGjQObMdHMmx1MTd0RXCQEKBdELCYvD84917ixFhUFzz4LL70EsbF+zSrlnvVo8raIr6qq4KmnDhQUrVrBc8/BqFE1BUU1b3YwNW1HcBEREU/98INxY237dkhOhvnz4bzzan7tz6xS7llPyPVYiFjKpk1w5pnGXIqDeylGj65TVMCBHUw92QTPm9eIiIgE3fvvwxlnGEXF0UfDqlW1igpwL9NSk+JITVLuhSIVFiLecDjgn/+Ek04yVnxKSjK6fD/4AFJTXb7Mmx1Mg7YjuIiIiDecTnjkEbj0UmOvpoEDjaKie/c6h7qTadOGHce0Ycq9UKTCQsRT27YZF81bboHSUuPnDRtqzaVoiDc7mDb2muqN8z5cl8OKLflaKUNERIKjtBTGjIG//914fNNN8PHH0LKly5e4k4MNHZMx+mSSm8Yq8yxIcyxE3OV0wptvwpQpUFgICQnG3IobbnCroDiYNzuYerpx3pWtNalNREQCaOdOGD7cWAUxJgZmzYJJk9x6qTs5WN8xe4sr6uzOrU3zrEOFhYg79u6FyZPh7beNx336wBtvwFFHef2W3uxgeuhrlmzIZXLmmjprfe8qKOPH0gKWbMjVhVZERPzvu++MomLnTmPRknffhf79PXoLd3Lw4GOWbMgl/c36M29y5hqXvf4SPBoKJRHB7nB6P1Toyy/hhBOMoiI6Gh56CL7+2qeiwh+0cZ6IiPjC62x8+21j4ZKdOyEtDbKyPC4qvGmrMs/61GMhYS+vqKzeoUKNdpuWlcH998MzzxiPjz4aMjONvSosoLGN8+DABkKe9oyIiEh4W7Ihl+mLPBxS5HDAtGnGRrAAQ4YYQ4STkgLeXk82i1XmmUc9FhLWlmzI5cffC+pcjKq7TZdsyK3/hRs3wmmnHSgqJk2CtWstU1SANs4TERHvVA+j9Sgbi4th5MgDRcXf/gYffhiUogKUeaEi5AqLjIwM0tLS6NWrl9lNEYur7jatj8tuU6cTXn4ZTjkFfvwR2rSBhQvhhRcgMTHwjfaANs4TMSgXRNzn1ZCi7duhXz947z2IjTWWV3/ySWN4cJAo80JDyBUW6enpZGdnk5WVZXZTxOI86TYFjAnaI0fC9dcby+cNGmQUF0OHBqfBHmpskyHQBkISGZQLIu7zOBu//RZ69YJ16yAlBZYuNZZXDzJtFhsaQq6wEHGXR92mX38NJ55orGrRpAnMmAFLlkA7664uoY3zRETEUx5l42uvwYABkJdnZGRWFpx+eoBbWD9lXmhQYSFhy53u0CiHnZ6v/tNYzWLHDmOlp2+/hTvvhCjr/+fR0AZCJxyerGX3RESkFnez8dTnH4fx46GiAi65BJYvhyOOCHwDG+DNBrMSXFoVSsJWdbcppfX/PmX/Hp7/+Bk6/rrOeGLcOHjuOWjePGht9AdXmwzNf/sts5smIiIWU52NuwrK6p1n0by8hBc+fpoO/1tlPPHAA8ZKUBa52ebNBrMSPCosJGxVd5sumL8eG9S6gPb7bR0zFz1Fm5J9xqTsF1+EMWNMaqnvvNlsT0REIk91Nk7OXFMnG4/Yt4s57zxEt/ztEB8Pr74KV15pVlNdUuZZlwoLCSt2h7PWXYxBaan87/BksvPjyS0oI8ph55Zv5nHTireJcjrh+ONhwQLo3t3spouIiATMofmYMbonD390YB+L07av58UPH6NFSSG0b28sJXvqqSa3WkKNCgsJG642+7myNSy/+xzWrvyJzjdPpM33K41fXn89zJwJTZua02AREZEgcJWPDww5lpaJcTSdO4cTFjxAVFWVsQLUBx8YxYWIh1RYSFio3uzn0PGiuwrK+LG0gO//tYDe990Iu3dDs2bw0kswapQpbRUREQmWhvLx5szv+CLnQzq9+S/jyVGj4JVXdMNNvKbCQkJeQ5v94HRw4fLPOWXZx+B0GMvlzZ8P3boFu5kiIiJB1VA+Ni/bT8aHT9Dpt7XGE488AvfeCzZNghbvqbCQkOdqs5+ksv08/dEzDPplNQB5I8aQ8vrLPt+JOXScqlajEBERK3KVj1325DDn3YfouieH4ibx/P7si3SffLVXn6FMlIOpsJCQV99mP2l//MrsDx6l075dVEbHcP+gKZxx/10M97GocDVOderQNK2fLSIillJfPp65dQ2zPnyC5PJifk9qy8TLHuCGvufizRImykQ5lDUWJfZARkYGaWlp9OrVy+ymiEUcutnPyB8/473MO+m0bxfbkw/j0WtuZv6J57m1KVBDqsepHnr3Z1dBGZMz17BkQ65P7y8i3lEuiNSvVu45nYz/biFzF0wjubyY7zocy8VXP8PGlCO9ykdlotQn5AqL9PR0srOzycrKMrspUg+7w8mKLfl8uC6HFVvysTvqnfngV9Wb/cRVVfLoklnM+PhZ4qsq+KJrLy4a/yzb23WkXbLRPeuthsapVj83fVF2UM5XRGpTLojVmZGNcCAfY+2VPPrJLKZ98RLRTgfv9DiX0Vc+Sn5iS6/yUZkormgolPiNWV2i0VE2Hu3TmqSxN3LKzp9xYOOZM8eQ0fdysBm189ShaT6N+XQ1TrWaE8gtKGP11j3atEdERGqYOVwoOsrG//U7jGZjbuW0HRtwYOOx/tfwcu9LsP01SdubfFQmiisqLMQvGlrObnLmGmaP7Rm4C+iKFQwYcxnk5lIY34ybL7qTZV2NTX3aJcdzQutkl5/t7qSz+sap1sfd40REJPyZmo0AGzZw7rhhsGMrxXEJ3Dj0byztagwZTG2guGksG5WJ4ooKC/FZY12iNowu0UFpqf5fKeKll+DGG6GyEo47jsT33mdSdCsuOehiOP/tt+p9qSd3kdwdf+rrPA4REQkPpmYjwOLFxr4U+/fDkUcS/8GHXJ/QjosbuZHmTjYqE8WVkJtjIdbjSZeo35SXw6RJxv8qK2HECFi5kuhuR9O3a2uGn9SBvl1bu7xYezrprHqcqqtLvw18nschIiLhw5RsBHA6YcYMGDbMKCrOPhtWrSL6+B6N5qO72ahMFFcsU1jk5eWRnp5udjPEC+52dX7zy27/TFzLy4NzzzV6K2w2ePRRY9O7Zs3cerk3k86io2xMHZoGUOdCWv3Y13kcIlKbckFCmbvZuKug1H8Tu8vKYPx4uOsuo8C4/nr49FNo06bRl3qSjcpEccUyQ6EWLFhAnz59zG6GeMHdrs5ZS7fU/Oz1xLUffjDuwmzfDsnJMG8eXHCBR2/h7aSzwT3aMXtszzpdxA2NUxUR7ykXJJS5m40Pf7SRPcUVNY+9zsddu+DSS2HFCoiOhpkzIT3d7Z20Pc1GZaLUxxKFxRdffEH//v1Zu3at2U0RL1R3ie4qKKv3Tkd9vJq49sEHMHYsFBdDt26wcCF093xLH18mnQ3u0Y5BaanaZVQkwJQLEurczcaDiwrwMh/XroXhw2HHDmjRAhYsgIEDPWqvN9moTJRDmT4Uqri4mF9//ZXjjjvO7KaIlxrqEnXFo3WunU5juNMllxhFxcCBsHKlV0UF+D7pLDrK5tY8DhHxjnJBwoE32Qhe7APx7rvQr59RVHTrBqtWeVxUgPfZqEyUg5leWLz22muMHTvW7GaIj6q7RFOT3V8Bwq2Ja6WlRi/F/fcbj2+6CT7+GFq29LqtmnQmYm3KBQkXrrKxVWKTBl/nVj46nfDQQ8biJSUlcN55RlHRrZtXbVU2ij+YOhRq7dq1HHPMMTRt2rTRY8vLyykvL695XFhYGMimiRcO7RLd/Md+Zi39pdHXuex+/eMPo2t31SqIiYFZs4xVoHxUfRdpcuYabFCri1qTzkTMpVyQcFPfcKFdhWXc9va6Rl/rMh9LSuCaa4yFSwBuuQWeesrISi8pG8UfbE6n05T91u12OzNnzuSOO+6oeS4zM9PlXapp06Yxffr0Os/PmTOHhIQEjz8/JyeHDh06ePy6UBfM895bXMH32/c2etwpR7SkZWJsreeSfv+ds2fMoNnu3ZQ3a8byW24hz8thEa7OOa+ojE279lNWZa95Lj4mmm6pzbxae9vphH0lFZTbHcRFR9EiIdbdOXMBEYl/xyPxnMH78y4pKWHChAkUFBSQlJQUgJZ5RrkgkcKXfGy6Zw9nPv00rbduxREdzXfXXMOWc87xW9v8kY1Wy0Nxn6+5YFph8e2337JixQpatz6w6s6KFSvo27cvvXv3Ji0trdbx9d2Z6tixo9cnPm/ePEaNGuX9CYSoYJ633eGk3xNfupy4ZsNYPeK/fxvA99v2Hpj49etaokeOgIICSjt14ZtnXyOxR5rXE8IaOmd3d95ujCeb7QVLJP4dj8RzBu/Pu7CwkOTkZMsUFsoFiRRe5+PuX4i+9BLIzaWyZStWPfki0QMG+H3CtC/ZaMU8FPf5mgumDYU6/fTTOf3002s9FxMT4/LOVFxcHHFxccFomviJO92qw05sx9kzltZcgEb++Cm9PskAh50fOh3H+GH3sXdFIaxYGZALU/WkM19Ubyh0aDh4tbKHSARTLkik8CYfh2Uvo+fHzxJdVcmWlM6Mu+Tv/P5LU/jF//nobTYqD8X0ydsS3lxNXEtNjuf6s7rw0ldbyS0ow+Z0cOdXrzPj438S47Dz4bFnc/mIh9mbkFzzGle7YpvJm832REREPM3Hfy56iriqSj47qjfDRz/J7y1Sa15jhXxUHgpYZB8LCW/1TVw7pVNLzp6xFCcQV1XBjP/MZNjGrwD4Z98reObMsXU29XFi3MmZviibQWmplphA5u1meyIiIo3lY0JFKf9Y/DTnb14JwPN9RvDUmVfhiIqu9T5WyEfloYDFCgstLxi+Du1WXbEln9yCMpLK9vPSe/9Hnx0bqIyK5r7zb2TBCYNcvo/VLky+bLYnIo1TLki4c5WPHQrymPPuQxy7+zfKo2O4Z/DNvN/D9SRts/NReShgscJCIkdeURmHFf3J3AXTOHb3bxTFNmXSJffzbeeT3H69Ffi62Z6IiMjB8orKOPX3n3jh/UdpU1LA7sQWTLrkftZ0ONbt15tBeSigwkJM0umP7bz3xt/oULSbvMSWjB85nezDjnT79Va5MFVvKNTYyh7aUEhERNxx3Cfv8ea8+4l1VLHhsK5MvPTv5Ca1dfv1ZuWj8lBAk7fFDN9+y4mjhtChaDdbWh3OpVc95XZRYbWdP6tX9gDq7FaqDYVERMRtdjvccQdH3XMzsY4qPu52OiNHP+F2UWF2PioPBVRYSLB9+CGcey62vXvZd8IpjBzzBDnJh7n1UqtemBpa2UNL64mISKMKCmDoUHjmGQB+mXw76RffQ1mse70PVslH5aFoKJQEz5w5MGkSOBxw0UW0ePttHv21oN6NdIad2I6FP+TWej7Vwhvs1Leyh783LBIRkTD0yy8wbBhs3AhNm8LcuRx1+eU872KjOavno/IwsoVcYZGRkUFGRgZ2u73xg8U6nnwS7r7b+HnCBJg9G2JiGNwjweUF6K7Bx4bUhckfm+2JiOeUCxKyli6FESNgzx7o0MHo1T/lFKDhf6BbPR+Vh5Er5AqL9PR00tPTa7YcF4tzOuG+++Dxx43H994LjzxSa48KVxcgV8/bHU5LX1BFJLiUCxKSXngBbroJqqqgd2/44ANoV7vHQfkooSbkCgsJIXY7pKfDiy8aj598Ev72N5/ecomLrmGrdAGLiIg0qLISbrsNMjKMx2PGwMsvG8OgfKB8FCvQ5G0JjIoK42L54otG78RLL/mlqJicuabOzp67CsqYnLmGJRtyfXp/ERGRgNqzBy644EBR8eij8MYbfikqlI9iBSosxP9KSuDii+Htt6FJE+P/J0706S3tDifTF2XXuzZ29XPTF2Vjd9R3hIiIiMl+/hn69IEvvoDERGPo07331hoa7A3lo1iJCgvxr8JCGDwYPv7YuAOzcCGMHOnz267euqfOnZiDOYHcgjJWb93j82eJiIj41ZIlRlGxeTN06gTffgvDh/vlrZWPYiUqLMR/9u2D886Dr7+GpCT49FOjyPCDvCLXF01vjhMREQk4pxNmzoQhQ4y9Kvr1g9Wr4YQT/PYRykexEhUW4h979sDAgbBqFbRsCV9+aVxA/SSluXubBLl7nIiISEBVVMD11xsTtR0OuOYa+PxzSEnx68coH8VKVFiI73bvhgED4PvvoU0bY13uv9bh9pfeXVrRLjkeVyNRbRirX/Tu0sqvnysiIuKx3buNm21z5kBUlLGj9iuvQFyc3z9K+ShWosJCsDucrNiSz4frclixJd+zCV67dkH//vDjj3DYYbBsGZx4ot/bGB1lY+rQNIA6F8/qx1OHpmm9bhER8YpPWXiw9euNfSmqhwUvXmz0Wvg4SdsV5aNYifaxiHCNrXvd4GY7OTlwzjmwaZOxY+iXX0K3bgFr6+Ae7Zg9tmed9qZqnW4REfGBO3tAuLX53MKFxlLr+/dD166waBEce2zA2698FKvwuLD45JNPOPfcc4mJUU0S6qrXvT70nkz1utfXn9WFhT/k1n+hTa4yeip+/RWOOMIoKrp2DXibB/dox6C0VO0sKmIhygUJZY1l4eyxPQEaLjycTmMT2HvvNX4+5xyYPx9a190dO1CUj2IFHqfAsGHDSExMZNiwYYwYMYLzzjuP2NjYQLStXhkZGWRkZGC324P2meHInXWvX/xqa53f7SooY9rsTzlz8XQSt2+FI480iopOnQLa3oNFR9no2zV4F2sRaZhyQUJVY1loA+55bz0FJZUuC48XR6Zx3swHITPT+MXkyfDss8Y+TkGmfBSzeTzH4s8//+Sll14iOjqaSZMm0bZtW0aPHs37779PaWlpINpYS3p6OtnZ2WRlZQX8s8JZY+teu9Jm/x7efOt+ErdvxdmlizGnIohFhYhYj3JBQpU7e0Dsq6eoqP5d2/17aH/JhUZRER1t7Kj9/POmFBUiVuBxYdG8eXNGjBjBK6+8Qk5ODp9++im///47I0aMoG3btowcOZJPPvkkEG0VP/JmPes2xXuZN+8+jtyTw+9JKayZ+x507BiA1olIKFEuSKjyZW+H43b9wgev306PHT9TldwCPvkEpkzxX+NEQpBXq0IVFRXx1ltvMWrUKM4//3x+/vlnJk6cyHvvvccZZ5zBddddx7333uvvtoofebqedevifbw5736O2vM7Oc3bMmrUo/ye1DZArRORUKNckFDk7d4OF/68nHf+fTfti/7kl1aHs+y1hXDuuX5unUjo8XiOxXnnncdXX31Fs2bNuPjii1mwYAHnnHMO0dHRNb8/7rjjuPTSS3nsscf83mDxj+p1r3cVlNXbxXuwliUFZL79d7rlbye3WWtGj3qEHS1StdmOiADKBQldnmQhgM3p4OZv3uK2b94EYFmXU7hp+F281CMtsA0VCREeFxbt27fn/fffZ9CgQS5XAOnVqxcvv/yyz42TwKle93py5hps4PKCmlxaxL/f/jvH7v6NP5q1YvSoR9nesr022xGRGsoFCVUNZWH14xYJTSgoqSSusoynPprJRf9bDsDLvS7m8f7XkNIyUXko8hePh0LNnTuXCy64oMFlBVu0aMGVV17pU8Mk8KrXvU5Nrt3z0C45nklndaFZeQmvLZhKWt5Wdie2YPSVj/Bbqw6ANtsRkQOUCxLKXGVhanI8L4ztyeOXHk9q4Z8s+PfdXPS/5VRExfC3C27m0XMm4IiKVh6KHESLjoeohjbqcWsTn7+4XPe6vIzrp02kde4m9jRNYvQVj7Cldcc6GwaJiIgEijt55knmudLgHhArV9J/wV3E/5lHftMkbrjkPrI69lAeitRDhUUIamiHUGhkE5961Fn3urISrriC1lnf4mzenN9ff5cbOx+rzXZERCRo3NkN251j3FXvHhBvvAETJxJfXo7z+OPZ9txrjE1O4XbloUi9VFiEmIZ2CL0hc029rzl099AG2e0wbhwsWgTx8dgWL+aEs87iBN+bLiIi4hZ3d8Nu7BivexMcDrjvPnjiCePxsGHYMjPp2bw5biSpSMTyarlZMYc7u2XXp/p30xdl42zwQCekp8O8eRATA+++C2ed5X2DRUREPORO1k1b+BPTFjZ8zPRF2dgd7qz1dIiiIrj44gNFxb33wvvvQ/Pmnr+XSIRRj4XFHTx29M+icq92ywbjQptbUMa+kgoXBzjhnnvgxRfBZjN2Eb3wQu8bLiIi4kJD8yLc2Q17V2F5g+9fnXmrt+6pO7ypIVu3wrBhsGEDxMXBK6/AmDHuv14kwoVcYZGRkUFGRgZ2u93spgRcfWNHfVVud9T/iyeegCefNH5+6SW44gq/faaISCBFUi6Eg8bmRfiyG/ahPHqvr7+GSy+FP/+E1FT44AM47TS/tUUkEoTcUKj09HSys7PJysoyuykBVT2+1J9FBUBcdD1/5HPnGl29ADNmwIQJfv1MEZFAipRcCAeusq16XsSSDbl+3XzV7fd65RVj5+w//4SePSErS0WFiBdCrrCIBA2NL/WWDeOOUIuE2Nq/+PjjA4XEXXfBnXf68VNFREQM7sydmL4om1M6taRdcjyu1luyAalJcaQmNXyMWxu5VlXBbbcZOVhZCZdfbvRcHH64O6ckIodQYWFBjY0vrY/Nxc8HP546NA3bwb9cvRpGjDBWgho7Fh57zIvWioiINM6duRO5BWV8v21vzfLprvJs2rDjmDas4WMa3bhu3z646CKYOdN4/NBD8NZbkJDQ+MmISL1UWFiQN+NLq3cIfcHF7qF1lt3bvBmGDIGSEjjvPKMbOEp/HUREJDDczba8orIGd8OuzjN3jnFp82bo0wc++QSaNoUFC+CBB6h9901EPBVyk7cjgbtjQh8YcixtmsfVWVHD5e6h1f74A84/3xhLesop8M47EBvr4lNERER85262VR/X4G7Yf3HnmDo+/9wY8rR3rzHkaeFCOPlkn85NRAwqLCyod5dWtEuOZ1dBWb1jUW0Yd2TGn9Gl3otnvbuH/iWmtNRYRnbrVjjySPjoI63NLSIiAeduth08L6KhPPPkmBoZGXDLLcYQ4D59jP0pUlPdPwkRaZDGvlhQdJSt0fGljY4drU9lJf1mzoQ1a6BtW6ML+LDDfG2uiIhIowKWbe6orIQpU+DGG42i4qqrYOlSFRUifqbCwqJ8GjtaH6cTbrqJduvXQ2Ki0VNx1FFet8/ucLJiSz4frsthxZZ873Y3FRGRiOL3bHNHfr4x/Hf2bGMOxRNPwGuvQbz/lrVVJooYNBTKwrwaO+rKP/4BL76I02bDNm8e9Orldbsa29xIRETEFb9mW2M2boShQ2HLFmjWDN5803jsR8pEkQNUWFicR2NHXfnww5r9KdaOHUtPHy6q1ZsbHXovpnpzo4DdcRIRkbDhl2xrzMcfw5VXQmEhdO4MixZBjx5+/QhlokhtGgoV7tasgdGjjaFQU6bwv8GDvX4rdzc3UhewiIiYxumEZ54x9qgoLISzzjL2bfJzUaFMFKkr5AqLjIwM0tLS6OXDUJ6I8fvvRpdvSQkMHgzPPuvTGt3ubm60euserz9DRMRTygWpUV4O110Hd9wBDoexo/ZnnxkLlviZMlGkrpArLNLT08nOziYrK8vspljb/v1GUbFzp3GX5u23Ica3kW+ebG4kIhIsygUBIC8Pzj0XXn3V2PD12WfhpZcCtk+TMlGkLs2xCEd2uzH8ad06SEmBxYshKcnnt/V0cyMREZGg+PFHGDYMtm2D5GSYPx/OOy+gH6lMFKkr5HosxA33329MUouPN3YU7dTJL29bvbmRq8FUNoyVMA7e3EhERCSgPvgATj/dKCqOPhpWrQp4UQHKRJH6qLAIN2+9ZazRDUZ38Gmn+e2tTd3cSERE5GBOJzz6KFxyCRQXw8CBRlHRvXtQPl6ZKFKXCotwsm4dXHut8fPddxvL7PmZKZsbiYiIHKy0FMaONXroAW66yVhetmXLoDZDmShSm6lzLPbv38/cuXOJjo6mSZMmxMXFcdVVV5nZpNC1ezdcfLFxsR08GB55JGAfFdTNjUQk4igbpEG5uUberV5tLEoyaxZMmmRac5SJIgeYWli88cYb3HDDDcT8tVrRpk2bWLp0KQMGDDCzWaGnshIuv9wYX3rUUcbOotHRdQ6zO5zsLa7gw3U5Pl/4grK5kYhEJGWDuPTdd0ZRkZMDrVrBu+9C//6NvszucAb0H/7KRBGDqYVFfHx8TXAAdOvWTcsFeuOOO2DZMmjWzNhlu56u4CUbcpm+KJu00r08+cs6wJhUNnVomrpqRcRSlA1Sr7ffhvHjoawM0tKMxUm6dm30ZdX5d/CeE8o/kcAwdY7F+PHj6zxXWVkZ/IaEsldfheeeM37OzDQutodYsiGXyZlr6mzks6ugjMmZa1iyITcYLRURcYuyQWpxOODBB415g2VlcOGFsGKF20WF8k8keEwtLGyH7AI9f/58zjzzzHqPLS8vp7CwsNb/It6qVXDDDcbP06bB8OF1DrE7nExflI2znpdXPzd9UTZ2R31HiIgEn7vZoFyIAMXFxlDfhx82Ht95p9FT4cbeTMo/keCzOZ1OU/+LKi4uZu7cuaxcuZLBgwczZsyYeo+bNm0a06dPr/P8nDlzSEhI8Phzc3Jy6NChg8evCxSnE/aVVFBudxAXHUWLhFhsDQz/jC0sZPD995OYn8+OU09l+a23GjuNHmJvcQXfb99b87hNVDF/OhLrHHfKES1pmRiY3UnNZrU/62CJxPOOxHMG78+7pKSECRMmUFBQQJIfNtH0J3eyIdxzIdR4mmONSfjzT856+mlabtuGPSaGrOuuY+vZZ7v9+kPzz5Vwzj8RT/maC6YXFgf7/vvvycnJYdiwYXV+V15eTnl5ec3jwsJCOnbs6PWJz5s3j1GjRvnUXn/xePynw2F0BX/yibEZ0Hffubx78+G6HG55a13N43NjN/NFxdF1jnv2ypMYflJ4BqqV/qyDKRLPOxLPGbw/78LCQpKTky1ZWBzMVTaEcy6EGr/PY1ixwtif4o8/ICUF3nsPzjjDo7c4NP9cCef8E/GUr7lg2lAou93OoTXNKaecQn5+fr3Hx8XFkZSUVOt/4cCr8Z+PPmoUFfHx8M47DXYJpzSPd/k7b44TEQkkT7IhXHMh1Ph9HsNrrxkrPf3xB5x4orGsrIdFBSj/RMxgWmHx008/sXr16jrPx8XFmdAac3g1/vOLL2DqVOPn2bPhhBMa/IzeXVrRLjm+zq6g1WwYd5V6d2nlYetFRPxP2RBa/DqPwW6Hu+4yVn6qqDB6LJYvh06dvGqb8k8k+EwrLI4//ni++OKLWnemysrKsNvtZjUp6FZv3VPnDs/BnEBuQRmrt+4xnti5E0aPNoZCXXutcfFtRHSUjalDjZWiDr24Vj+eOjRNG/mIiCUoG0KLxznmSmGhsQDJjBnG47//3eiRb9bM67Yp/0SCz7R9LGw2G+PHj2fmzJnEx8cTFxdHVVUV48aNM6tJQZdX5PpiXOe4ykq44grIyzN6KWbNcvtzBvdox+yxPZm+KBtKDzyfqnW8RcRilA2hxaMcc+XXX2HoUMjONob4vvqqsbSsHxycfwcXQMo/kcAwdYO89u3bc9ttt5nZBFN5NP7z/vuNLuHmzY27OE2bevRZg3u0Y1BaKi/+63eGnXpSQHYeFRHxh0jPhlDi8zyGZctgxAjIz4d27YxNXnv18l8DOZB/gdx5W0QMphYWkcjucNZc3NokxpGaFM8fhWX1jk+1YdxV6b1++YHu4VdfNVaC8kJ0lI2WibFa/UJERNxycGbV9w/y6nkMuwoaybH65jG89BKkp0NVFZx6KnzwAQRoud/oKBt9u7YOyHuLyAEqLIKovuX4WiQ0wYlx8T34olx92X6sVzLRl480HtxyC1x2WZBaKyIikcydJWSr5zFMzlzjMsfqzGOoqoLbb4fnnjMeX3kl/OtfHvfEi4j1mLrzdiRxtRxfQUklAMkJTWo9n5ocz+xRJ9L//+6EvXuNuzlPPhm09oqISOTyZAnZ6nkMqcm1hzulJscze2zP2vMY9u419mGqLioefhjefFNFhUiYUI9FEDS2HJ8NiI+J4t8TTuPP/eUHupsffwz++19ITIR58yBWO4OKiEhguZNZ0xdlMygttaYnwq15DP/7HwwbBps2QUICZGYaS8qKSNhQYREE7izHt6uwnCib7cD8h1Wr4MEHjZ8zMuCoowLfUBERiXieLCF78LyFBucxfPopXH45FBRAx46wcCGcdJJ/Gy4ipgu5oVAZGRmkpaXRy8+rRgSSx8vxFRYa+1XY7cbY06uvDmDrRERCWyjmgpX5ZQnZak4n/POfcMEFRlFx+umQlaWiQiRMhVxhkZ6eTnZ2NllZWWY3xW0eL8eXnm6s692pk7G7tk1L4omIuBKKuWBlPi8hW62iAiZNMhYecThg3Dj48ks47DA/tFJErCjkCotQVL0cn6vywIax0kbvLq2MMaeZmRAVZUxoa9EiiC0VEZFI51FmufLnnzBoELz8snFzbMYMY7n0uLhANFlELEKFRRBUL8cH1LlQ11qO77etMGXKX09MNbqMRUREgsjtzHK1wdyGDdC7N3z1lbGp66JFcOed6n0XiQAqLIKk0eX4jmkLY8ZAURH06wf33WdSS0VEJNJ5tITswRYvhr59YetWOPJIWLEChgwJQotFxAq0KlQQNbgc36OPwsqVkJxsDIWK0R+NiIiYx60lZKs5nfDUU3D33cbPZ58N77wDbdoEv+EiYhr96zXI6l2O78cfYdo04+fnnjMmbYuIiJiswSVkq5WVGZO0X3/deHz99UaWae8lkYijwsJsFRXGShmVlTB8OIwda3aLRERE3LNrF1x6qTHkKToaZs40VjbUfAqRiKTCwmyPPALr1kHr1vDii7oYi4hIaFi71rghtmOHsYLh/PnGSlAiErE0edtM339vFBYAzz+vtb1FRCQ0vPuusdDIjh3QrRusWqWiQkRUWJimvNwYAmW3w8iRcPnlZrdIRESkYU4nPPwwjBgBJSVw3nnGwiPdupndMhGxAA2FMsvUqfDTT5CSYvRWiIiIWFlJCVx7Lbz9tvH4lluMlaC0iqGI/CXkeiwyMjJIS0ujV69eZjfFeytXGruQgjGvQsvxiYh4LSxywepycuCss4yiIiYGXnrJmKitokJEDhJyhUV6ejrZ2dlkZWWZ3RTvlJYaQ6AcDmMFqIsvNrtFIiIhLeRzweqysqBXL2NeYOvW8PnnMHGi2a0SEQsKucIi5E2bBps2Qfv28M9/mt0aERER1+bNM3oqcnPhuOOMIuPss81ulYhYlAqLYPrhB3j6aePn2bOhZUtz2yMiIlIfhwP+/ncYPdrYAO+ii+Dbb6FLF7NbJiIWpsGRbrA7nKzeuoe8ojJSmsfTu0sroqM83G/Cbje6ju12uOwyGDYsMI0VEZGQ4peM8af9++Gqq+CDD4zHd99tLI0eHW1em0QkJKiwaMSSDblMX5RNbkFZzXPtkuOZOjSNwT3auf9Gzz9vdCEnJWkIlIiIAH7MGH/Zts248fXjjxAbC3PmGEWGiIgbNBSqAUs25DI5c02tCz7AroIyJmeuYcmGXPfeaMcOuO8+4+fHHzfmV4iISETzW8b4y/LlxiTtH380NmxdtkxFhYh4RIWFC3aHk+mLsnHW87vq56YvysbuqO+Igw92wo03Gl3Lp58Okyb5u6kiIhJi/JYx/vLqq3DOObB7N5x0EqxeDX37BuezRSRsqLBwYfXWPXXuIh3MCeQWlLF6656G3+j992HhQmOt7xdfhCh95SIikc5vGeMrux3uuMPY+K6y0pgDuHw5HHFEYD9XRMKS/pXrQl6R6wu+28cVFMBNNxk/33039Ojhh5aJiEio80vG+KqgAIYOhWeeMR4/+CDMnw+JiYH7TBEJa5q87UJK83jfj7vvPti5E446Cu6/308tExGRUOeXjPHFL78Yk7Q3boT4eJg7F664IjCfJSIRI+R6LDIyMkhLS6NXr14B/ZzeXVrRLjkeVwv+2TBW7ujdpVWd39kdTtYvWIJz9mzj8ewXoGnTwDVWRCSCBSsX/MmXjPGF3eHkp8wPqDi1F2zciLN9e/j6axUVIuIXIVdYpKenk52dTVZWVkA/JzrKxtShaQB1LvzVj6cOTauz1viSDbmc9dhnRN2Yjs3p5J0e59Ivi+Cv7iEiEiGClQv+5G3G+GLJhlyevvQ2uo0bQWzBPta1O5phVz/DkvgOfvsMEYlsIVdYBNPgHu2YPbYnqcm1u6JTk+OZPbZnnTXGq5cO7P/VhxyX9ysFcYk8OuBa85YOFBERy/I0Y3zxydrt5I2byF0fPksTh50Pjz2bK0Y9zgZnM+WTiPiN5lg0YnCPdgxKS210V9TqpQOTSou486s3AHjmzLHsSUgGjDtQ0xdlMygt1dwdVUVExDLczRhf2P/Mp9XIizl/y1oAnjzrap7vMxJsxmcon0TEX1RYuCE6ykbfrq0bPKZ66cDpyzNpWVbEz206kXnyhTW/P3jpwMbeS0REIoc7GeO1n3+mYvCF9Nq2leIm8dx20R182q32/hTKJxHxFxUWfpJXVMYxeVsZu/ZjAKYPnIQ9Krre40RERAJuyRK48kqaFhTwe1IKEy57gJ9Turg8XPkkIr5SYeEnKc3imP75i0Q7HSzu3o8VnU6o/7hALR0oIiIC4HTCs88aG985HBSe2ofhfW4kP7FFgy9TPomIrzR5209Oy/qc03ZsoDQmjkfPubbO7wO1dKCIiEiNigq4/nq47TZwOOCaa0j8aimx7VODvrStiEQeFRb+UFxM1F1/A2B2nxHkJqXU+nWglg4UERGpsXs3DBwIc+ZAVJSxo/YrrxDdND7oS9uKSGRSYeEPjz8Ov/8OnTvT4x8PBWXpQBERkRrr10Pv3sZmd0lJsHix0Wvx18pPwVzaVkQil+ZY+OrXX2HGDOPnZ57hvFOP5NyeXQK6dKCIiEiNhQthzBjYvx+OOsp4fOyxdQ4LxtK2IhLZVFj46vbbobwcBg2Ciy8GArx0oIiICBiTtJ98Eu691/j5nHNgwQJo5XquhPJJRAIp5IZCZWRkkJaWRq9evcxuitHl/OGHEB0NM2fWdDmLiEjwWCoXgqWsDK6+Gu65xygqpkwxlpdtoKgQEQm0kCss0tPTyc7OJisry9yGOJ1w113GzxMnQlqaue0REYlQlsmFYMnNhf79ITPTuLGVkWH8r0kTs1smIhFOQ6G89d57sHIlJCbC1Klmt0ZERCLBmjUwfLixYEjLlvDOO8YQKBERCwi5HgtLqKw0xrSCsQFRaqq57RERkfC3YAH062cUFcccA6tXq6gQEUtRYeGNOXNg82ZISYE77zS7NSIiEs4cDpg+HS6/HEpLYfBgo8f8qKPMbpmISC0aCuWp/fuNCzzAgw9C8+bmtkdERMJXSQmMH2/0VoCxEuGTTxpzK0RELMbUwmLbtm0sXLiQhIQEKisr6d69OwMGDDCzSY17+mn44w/jTtH115vdGhGRsBOS2RAIO3YY8ynWrjUmZr/wAlx7rdmtEhFxydTC4qOPPuKmm26qefzee++xe/du2rZta2KrGvDHHwc2w3vkEa3AISISACGXDYGwcqWxN9Iff0CbNvD++8b8ChERCzNtjsXPP/9M7969az13zjnnsHr1apNa5IaHHoLiYujVC0aONLs1IiJhJySzwd/eeMNYTvaPP+D44yErS0WFiIQE03osDj/8cGJjY2s9V1paSlxcnEktasTmzfDSS8bPTz6pzfBERAIg5LLBnxwOuO8+eOIJ4/GwYcZeFZrLJyIhwrQei2bNmtUJj88//5wzzzzTpBY14v77oaoKLrzQuJMkIiJ+F3LZ4C9FRcbQp+qi4t57jeFPKipEJIRYZlWo7du306JFC5d3pcrLyykvL695XFhYGKymwfffGyty2Gzw+OPB+1wRkQjXUDaYmgv+tHWr0TuxYQPExcErr8CYMWa3SkTEYzan0+k0uxGVlZW89NJLpKenuzxm2rRpTK9e5vUgc+bMISEhwePPzMnJoUOHDm4de+ZTT3H4mjVs7dePlVOmePxZVuLJeYeLSDxniMzzjsRzBu/Pu6SkhAkTJlBQUEBSUlIAWuabxrLBzFzwl7YbN9Jv5kzii4oobdGCr2+/nXztTyEiJvE1FyxRWMyePZurrrqKZs2auTymvjtTHTt29PrE582bx6hRoxo/8Pvv4dRTISoKNm6Ebt08/iwrcfu8w0gknjNE5nlH4jmD9+ddWFhIcnKyZQuLxrLBtFzwlzlzYMoUqKyEnj3hww/h8MOD9/kiIofwNRdMHwq1cOFCBgwY0GBRARAXF2fO5L3qu2FjxtQpKuwOJ6u37iGvqIyU5vH07tKK6ChN6hYR8ZU72WBaLviqqgruvBOefdZ4fPnl8Oqr4GEvizJIRKzG1MLixx9/JCYmhmOOOcbMZri2Zg0sWmT0Vvz977V+tWRDLtMXZZNbUFbzXLvkeKYOTWNwj3bBbqmISNiwfDb4Yt8+uOIK+PRT4/FDDxn54uFKg8ogEbEi0woLp9PJ1KlTGTJkCHPmzKl5PjEx0TpDGap7K0aPrtVbsWRDLpMz13DoGLJdBWVMzlzD7LE9dWEXEfFCSGSDtzZtMiZp/+9/0LQpvP46jBjh8dsog0TEqkwrLGw2G++//75ZH9+4tWth4cI6vRV2h5Ppi7LrXNABnIANmL4om0FpqeqSFhHxkOWzwVuff25srLpvnzGPYuFCOPlkj99GGSQiVmbaPhaWV91bMWoUdO9e8/TqrXtqdT0fygnkFpSxeuueADdQREQsz+mEjAwYPNgoKvr0MXbS9qKoAGWQiFibCov6rF1rrM5Rz9yKvCLXF3RvjhMRkTBVWWms+nTjjWC3w1VXwdKlkJrq9Vsqg0TEykxfFcqSHnrI+P8rr4RDJg+mNI936y3cPU5ERMJQfr4xf2LZsgObq/7tbx5P0j6UMkhErEw9FodauxY++MC4+D/wQJ1f9+7SinbJ8biKBhvGyhy9u7QKZCtFRMSqsrOhd2+jqGjWzOgBv+sun4sKUAaJiLWpsDhUdW/FqFF1eisAoqNsTB2aBlDnwl79eOrQNE2aExGJRP/5jzGP4tdfoUsXWLEChg7129srg0TEylRYHGzdugO9FYfMrTjY4B7tmD22J6nJtbuaU5PjtcyfiEgkcjrh6afhoougqAjOOgtWr4YePfz+UcogEbGqkJtjkZGRQUZGBna73f9v/sQTxv9fcQUce2yDhw7u0Y5Baana9VRExGQBzQV3lJfDDTfA3LnG4wkTjJWgYmMD9pHKIBGxopArLNLT00lPT6ewsJDk5GT/vfFvv8GCBcbP99zj1kuio2z07draf20QERGPBSwX3JGXB5dcAt9+a6wk+MwzcPPNfplP0RhlkIhYTcgVFgEzc6axHOCgQXDiiWa3RkRErO6HH4ydtLdvh+RkmD8fzjvP7FaJiJhGcywA9u6FOXOMn++809y2iIiI9X3wAZxxhlFUHH00rFqlokJEIp4KC4AXX4TiYjjhBKPHQkREpD5OJzz6qDH8qbgYBg40ioru3c1umYiI6VRYlJfDs88aP995Z1DGxYqISAgqLYUxY+D++43HN90EH38MLVua2y4REYvQHIs334Rdu6BDB2M1KBERkUPt3AkXXwxZWRATA7NmwaRJZrdKRMRSIruwcDrhqaeMn2+9NaBLA4qISIj67jsYPtwoLlq1gnffhf79zW6ViIjlRPZQqI8/huxsaN4cJk40uzUiImI1b78NZ55pFBVpacamdyoqRETqFdmFRXVvxfXXG0sFioiIADgc8OCDcOWVUFYGF14IK1ZA165mt0xExLIidihUy19/haVLjbGyt9xidnNERMQqiovh6qvhvfeMx3feCY8/DtHR5rZLRMTiQq7HIiMjg7S0NHr16uXT+xz70UfGD1deCR07+qFlIiJiBn/lAmDsS3HGGUZRERsLr74KM2aoqBARcUPIFRbp6elkZ2eTlZXl/Zv89hsdV60yftaGeCIiIc0vuQC02bQJevUydtROSYEvv4Tx4/3TSBGRCBCZQ6GefZYoh8PYDO/EE81ujYiImO211zjn//4PqqqMXPjwQ+jUyexWiYiElJDrsfBZVRW8/77xs3orREQE4Ntvia6qMnbUXr5cRYWIiBcir8ciJgZ++okVf/sbfQcNMrs1IiJiBc89xyqnk9NeeAGiIu+em4iIP0Tm1TMxkd/OPBNsNrNbIiIiVhAby68DBqioEBHxga6gIiIiIiLiMxUWIiIiIiLis8ibY9EAu8PJ6q17yCsqI6V5PL27tCI6SsOlRESkYcoPEREVFjWWbMhl+qJscgvKap5rlxzP1KFpDO7RzsSWiYiIlSk/REQMGgqFEQqTM9fUCgWAXQVlTM5cw5INuSa1TERErEz5ISJyQMQXFnaHk+mLsnHW87vq56YvysbuqO8IERGJVMoPEZHaQq6wyMjIIC0tjV69evnl/VZv3VPnTtPBnEBuQRmrt+7xy+eJiIh/+TsX3KX8EBGpLeQKi/T0dLKzs8nKyvLL++UVuQ4Fb44TEZHg8ncuuEv5ISJSW8gVFv6W0jzer8eJiEhkUH6IiNQW8YVF7y6taJccj6tFAW0Yq3v07tIqmM0SERGLU36IiNQW8YVFdJSNqUPTAOqEQ/XjqUPTtB65iIjUovwQEakt4gsLgME92jF7bE9Sk2t3V6cmxzN7bE+tQy4iIvVSfoiIHKAN8v4yuEc7BqWlaudUERHxiPJDRMSgwuIg0VE2+nZtbXYzREQkxCg/REQ0FEpERERERPxAhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPgs5AqLjIwM0tLS6NWrl9lNERERC1AuiIhYQ8gVFunp6WRnZ5OVlWV2U0RExAKUCyIi1hByhYWv7A4nK7bks6uwjBVb8rE7nGY3SURETKRcEBHxj4jax2LJhlymL8omt6CMc2MLePbllbRLjmfq0DTtjioiEoGUCyIi/hMxPRZLNuQyOXMNuQVltZ7fVVDG5Mw1LNmQa1LLRETEDMoFERH/iojCwu5wMn1RNvV1blc/N31Rtrq/RUQihHJBRMT/LFFYrFixgq+++ipg77966546d6QO5gRyC8pYvXVPwNogIiLuUy6IiIQeU+dYLF68mG3btnHWWWfxww8/BOxz8opch4c3x4mISGAoF0REQpephcWQIUOw2WwAAQ2QlObxfj1OREQCQ7kgIhK6TB0KVR0egda7SyvaJcfj6tNsQLvkeHp3aRWU9oiISP2UCyIiocsScyzcUV5eTmFhYa3/uSs6ysbUoWkAdUKk+vHUoWlERwUn0ERExHfKBRERawmZfSwee+wxpk+fXuf5BQsWkJCQ4NZ73HpkGZt27aesyk6bqGLOjd1MfEw03VKbsXf9Muat93OjLSgnJ4d58+aZ3YygisRzhsg870g8Z/D+vEtKSgLQmuBRLoiI+JevuWBzOp2WWEsvMzOTsWPHuvx9eXk55eXlNY8LCwvp2LEjBQUFJCUluf05doeT1Vv3sPLzhfQZOIzeXVpF1B2pefPmMWrUKLObEVSReM4QmecdiecM3p93YWEhycnJHl9Hg0W5ICISXL7mQsj0WMTFxREXF+fz+0RH2ejbtTW/rY6nb9fWfmiZiIiYQbkgImItITPHQkRERERErEuFhYiIiIiI+EyFhYiIiIiI+MwyhUVDE/RERCTyKBdEREKLZQoLEREREREJXSosRERERETEZyosRERERETEZyGzj8Whqvf1Kyws9Or1JSUlXr82lEXieUfiOUNknncknjN4f97Vr7HIPqk+Uy6IiPjG11ywzM7bnvr999/p2LGj2c0QEQl5O3bs4PDDDze7GT5TLoiI+Ie3uRCyhYXD4WDnzp00b94cm81Gr169yMrKcuu1hYWFdOzYkR07dni0Xbknn2HF470570C3KdCfES5/1p6+Rn/W+rN25/2dTidFRUW0b9+eqKjQHxl7aC54wtu/PxIavPnvMBKEw/di5XMws23efravuRCyQ6GioqJqVVLR0dEeh0FSUpJHr/H0M6x2fDVPzjsYbQrGZ4T6n7W3r9GftfltsvqfdXJyskefY2WH5oI3PP37I6HB27wMd+HwvVj5HMxsmy+f7UsuhP4tqr+kp6db7jOsdrw3gtGmSDzvYHxPgX5//VkH5nhvX2Ol9xexGv2dr184fC9WPgcz22bWZ4fsUChfFBYWkpycTEFBgWWr3ECIxPOOxHOGyDzvSDxniNzz9jd9jyIivgubHgtPxMXFMXXqVOLi4sxuSlBF4nlH4jlDZJ53JJ4zRO55+5u+RxER30Vkj4WIiIiIiPhXRPZYiIiIiIiIf4XsqlAiIiIiwbJkyRLi4+MpKSnhtNNOo3Xr1mY3yXTh8p2Ey3n4k7ffiYZCiYiIiDRg8+bNxMXFccQRRwCwdOlSBgwYYHKrzBUu30m4nIc/+fKdRGyPxYoVK6isrOSss84yuylBsW3bNhYuXEhCQgKVlZV079497P/D2b9/P3PnziU6OpomTZoQFxfHVVddZXazgiovL4/p06eTkZFhdlMCbsqUKfTs2bPmcWJiIqNGjTKxRcFRUlLC66+/js1mo2vXrgwcONDsJoUd3c00TyCyy1X+V1ZW8tJLLxEbG4vD4eCII47gggsuACAnJ4f+/fvXHBsdHe1TG3wRiGwz+zvxV1aZfR7+4O9rerC/k4grLBYvXsy2bds466yz+OGHH8xuTtB89NFH3HTTTTWP33vvPXbv3k3btm1NbFVgvfHGG9xwww3ExBh/zTdt2hRxdyIWLFhAnz59zG5GwO3fv5/zzz+f4cOHm92UoKqqqmLGjBnccccdNGvWzOzmhKXNmzeTlpamu5km8Wd2NZb/8+fPZ/z48SQmJtYcv3PnTtq3b1/nWIfD4fHn+4s/s80q34mvWWWV8/CVP6/pZn0nETd5e8iQIaSnp3P88ceb3ZSg+fnnn+ndu3et58455xxWr15tUouCIz4+vubCC9CtWzd27txpYouC64svvqB///7YbDazmxJweXl5YV0ku/Lmm28yZcoUFRUeWLFiBV999VWt5yorK8nIyODll1/mxRdf5OOPP675XU5OTk1RAebfzYwk/s6uxvK/srKy5h9ZABdeeCFffPEFgKWuo/7MNit8J/7IKiuchz/485pu1ncScYWFlf4CBcvhhx/OCSecUOu50tLSsF+vffz48XWeq6ysDH5DTFBcXMyvv/7KcccdZ3ZTgmL37t2kpKSY3YygKykpiciCyhuLFy8mIyODZs2asX379lq/q75zN3HiRCZNmoTdbnf5DzUz72ZGGn9nV0P5X1FRUecfc1FRUTX/gG/fvj3btm2r+V1VVZVXbfAHf2ab2d+Jv7LK7PPwF39e0836TiJuKFQkqq/y/fzzz7n88stNaE3wHPof1fz58znzzDNNak1wvfbaa1xzzTVmNyNodu/eTX5+PsuXL8dms9GpU6da40PDUUVFBQkJCSxbtoxt27Zht9tJS0uLiKFv3hgyZEjNNeHQYQH13bn797//zVVXXRWRN6OsIpjZ5arXs7qQPProo1myZAlbt26lpKSkTk9KMAUr24LxnQQjq0LlzzaY1/RAficR12MhsH37dlq0aBH2PRZg3A3JyMjgqquuorKykq5du5rdpIBbu3YtxxxzDE2bNjW7KUHTuXNnjjzySMaPH8+4ceNo1aoVixcvNrtZAZWfn8+qVavo1KkT48aN49prr6W0tJRvvvnG7KZZkqsCIZTuZkY6V9lVUVHBM888U+u5WbNmUVRU5PZ7V1VV1TvM7eCFMwcPHkz//v258MILadOmjYet96/Gsi0UvhN3sioUzsNf3L2mW/07UWERYSorK1m0aBFDhw41uylBkZiYSHp6Om+88QbHHHMMCxcuNLtJAWW32/nyyy8555xzzG5KUPXo0YNjjjmm5vEJJ5xAfn6+iS0KvPLycgYOHEiXLl1qnhswYACbN282sVWhx507dxs3bmTZsmX85z//4aSTTgpyCwUazq7Y2FhGjhzJ7NmzAXj11Vc577zzaN68udvvHxMTg91u91t7A62xbLP6d+JuVln9PPzJ3Wu61b8TDYWKMHPmzGHcuHFmNyPg7HY7UVFRte5SnnLKKfz4448mtirwVq1aBcDcuXNrnluxYgVVVVX07t2btLQ0k1oWfAdPbgxHsbGxtGjRos7zmlzsGXfv3Im5Gsuujh07cvbZZ3PTTTdxzTXX0K1bN4/ePyUlpeb6aWWeZJuVvxNPssrK5+FPnlzTrfydhHfySi0LFy5kwIABEbGCzE8//URpaSmnnXZarefDffjX6aefzumnn17ruZiYGMaOHWtSi4LjnXfeYcSIEbWei4oK7w7Zww47rM7qRhA5CxT4S6jczYxk7mbXjh076N69O9u3b6+1p407YmNjKSwsrPWcw+Gw3H9PnmabVb8TT7PKqufhT55e0636nYR38kqNH3/8kZiYmFrDRcLZ8ccfzxdffFHrrmNZWZn+ARGmkpKS+OWXX2oeOxwOSktLTWxR4EVHR1NaWkpJSUnNc9u2bYuIGwf+lJKSwp9//ml2M8QFd7NrxYoV2O12brzxRlq0aMHnn3/u8Wc1adKk1jj1xYsXW27PEk+yLVy+k3A5j8Z4ck238neiHosI4HQ6mTp1KkOGDGHOnDk1z4fzzsQ2m43x48czc+ZM4uPjiYuLo6qqKiKGgUWi8847j3nz5rFs2TJsNhtlZWWMGTPG7GYF3NixY3n99dex2+04nU6ioqKYMGGC2c0KKaFyNzMSuZtdOTk5/P7774wcORKA/v3789FHH7Fp0yaPhohcccUVvPDCC8THx1NZWUmHDh3o3Lmz387HH9zNtnD5TsLlPNzlzjXd6t+JzXlw2SsiIhLmMjMzaw25yMzMZPjw4TWTHxcuXMgJJ5xgyX94iIhYmXosREQkooXK3UwREatTj4WIiIiIiPhMk7dFRERERMRnKixERERERMRnKixERERERMRnKixERERERMRnKixERERERMRnKixERERERMRnKixERERERMRnKixERERERMRnKixE/Oztt9+madOmbN++HYCvv/6a6OhovvvuO5NbJiIiVvCf//yHzMxMl793OBxMmDCB0tLSILZKxHcqLET87IorruCMM87gvvvuw+FwcOutt3L99ddz6qmnmt00ERHxM5vNxrJly9w+fv369UyePJk+ffq4PCYqKopWrVoxZcoUP7RQJHhizG6ASDjKyMjgxBNPpGXLluzYsYPPP//c7CaJiIgFpKen8/DDD3PUUUc1eNzDDz9M9+7d+eqrrzjrrLOC1DoR36jHQiQAunfvzu23386sWbN4/PHHadmypdlNEhERk61cuZLffvuNMWPGNHpsXFwcU6ZM4bHHHgtCy0T8Q4WFSIDs27cPgIKCAnMbIiIiQTF+/HjGjRvH6NGjSUxMpGvXrnz88cc1v58/fz4XXHAB0dHRAEyePJnjjz8eu90OwEMPPUSHDh0oKioC4OKLL+bzzz9n7969wT8ZES+osBAJgO+++45XXnmFp556iqlTp7Jz506zmyQiIkGQmZnJWWedxfr16zn//PO57rrran737bff0rt375rHjz76KH/88QevvvoqO3fu5Mknn+SZZ56hefPmAHTr1o2EhASysrKCfh4i3lBhIeJnDoeDyZMnM2HCBO644w5OP/10brvtNrObJSIiQXDJJZdwww03cOSRR3LTTTeRm5vL7t27Afjll19ISUmpObZly5Y88cQTPPjgg9xyyy306dOHK664otb7denShc2bNwf1HES8pcJCxM9eeOEFNm/ezPTp0wF46qmnePfdd/nss89MbpmIiARas2bNan5u2rQpAMXFxYAxNLa6N6La+PHj6dKlCx9++CGzZs2q837NmzfXkFoJGSosRPxsypQp7Nu3jzZt2gDQo0cPqqqqGDRokMktExERM8XFxdXMv6tmt9vZv38/dru9pgA5WFlZGbGxsUFqoYhvVFiIiIiIBEFKSgp//PFHref++c9/UlhYyE033cTkyZNxOBy1fv/nn39y2GGHBbOZIl5TYSEiIiISBCeddBK//vprzeOdO3cybdo0nnzySR566CF+++03XnzxxZrf79+/n99//50TTzzRjOaKeEyFhYiIiEgQDB48mMWLF9c8vvXWWznhhBMYOXIkSUlJPPTQQ9x3333k5eUBsHz5clJTUzn++OPNarKIR2xOp9NpdiNEREREwt2+ffvo3Lkz3377LWlpaY0ef+WVV9K9e/eaxUBErE6FhYiIiEiQPPnkk6xYsYL333+/weN++OEHhgwZQnZ2NklJSUFqnYhvNBRKREREJEjuvPNOKioqeOONN1we43A4uOKKK8jMzFRRISFFPRYiIiIiQVRZWcmuXbvo2LGjy2O2bNlC165dg9gqEd+psBAREREREZ9pKJSIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPhMhYWIiIiIiPjs/wGVn6djtFDvOwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(121)\n",
    "plt.scatter(x_samp, y_samp, label = 'Data')\n",
    "plt.plot(x_samp, y_fit, \"r\", label=\"Fitted\")\n",
    "plt.legend()\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.scatter(x_samp, y_samp, label = 'Data')\n",
    "plt.plot(x_samp, y_fit, \"r\", label=\"Fitted\")\n",
    "plt.xscale('log')\n",
    "plt.xlabel('ln(x)')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.tight_layout()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
